Slow growth thermodynamic integration

However, even with a small rate for the constraint change, the reaction barriers obtained from thermodynamic integration by the slow-growth simulations are dependent on the choice of the reaction coordinate. First of all, an unfortunate choice of the reaction coordinate may correspond to an unfavorable reaction path, which does not pass the transition state region, and thus leads to a substantial overestimation of the barrier. 

The primary methods for calculating free energies—free energy perturbation (FEP), thermodynamic integration (TI), and slow growth (SG)—have been extensively described in the literature. -s Since the FEP method is used in most of the calculations cited in this review, the theoretical basis of the methodology is described in this section. 

DCE = 1,2-dichloroethane FEP = free energy perturbation pmf = potential of mean force QM = quantum mechanics SG = slow growth THF = tetrahydrofuran TI = thermodynamic integration. 

Equation (4) is the fundamental equation of thermodynamic integration (TI). When the derivative of the potential energy with respect to X is known analytically, equation (4) can be applied via a numerical quadrature for a series of X values. In practice, equation (4) has mostly served as the basis of the slow growth (SG) procedure used with MD simulations. Specifically, X is changed incrementally over the full M time steps of the simulation and the average in equation (4) is approximated by a finite difference between the time steps to yield... 

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